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International Conference on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes

AAECC 1985: Algebraic Algorithms and Error-Correcting Codes pp 326–332Cite as

Polynomial factorization over ℤ[X]

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 229))

Abstract

This paper gives a new method of factorization of a polynomial P over ℤ. The method is grounded on the fact, that any squarefree polynomial has a simple p-adic root. The algorithm starts from a simple root of P over ℤ/pℤ and from this root the algorithm computes the corresponding root of P over ℤ/pk ℤ, using Newton's method. So we obtain a linear factor of P.

Afterwards, as Lenstra in [3], we search for a polynomial Q which is a multiple of this linear factor and which has sufficiently small coefficients. If k is sufficiently large, then Q is a divisor of P over ℤ.

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6. Bibliography

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Author information

Authors and Affiliations

  1. Centre De Recherche En Informatique De Nancy, B.P. no 239, 54506, Vandoeuvre-Les-Nancy Cedex, France

    Guy Viry

Authors
  1. Guy Viry
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Editor information

Jacques Calmet

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© 1986 Springer-Verlag Berlin Heidelberg

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Viry, G. (1986). Polynomial factorization over ℤ[X]. In: Calmet, J. (eds) Algebraic Algorithms and Error-Correcting Codes. AAECC 1985. Lecture Notes in Computer Science, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16776-5_737

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  • DOI: https://doi.org/10.1007/3-540-16776-5_737

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16776-1

  • Online ISBN: 978-3-540-39855-4

  • eBook Packages: Springer Book Archive

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